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International Meeting on Instabilities and Dynamics of Lasers and Nonlinear Optical Systems

Routes to Chaos in Passive All Optical Resonators Containing Molecular Gases

Robert G. Harrison, W. J. Firth, I. A. Al-Saidi, E. Cummins

Published Jan 1, 1985• 0 citations
Publisher

Abstract

There has been considerable interest over the last few years in transitions to chaos in passive optically bistable systems. Ikeda1 showed in 1979 that an optically bistable ring resonator containing the simplest of nonlinear systems, a two-level media, can show a period doubling route to chaos. This was demonstrated by us2 using NH3 gas near resonantly pumped by pulsed CO2 laser radiation. More generally we identified and demonstrated the unique advantages of molecular gases in this field, providing in particular a vast range of laser-molecular coincidences together with control of response time, and therefore switching time and modulation frequency, by varying gas pressure. Subsequent extension of this work to all optical Fabry-Perot resonators revealed huge oscillatory effects3 leading to chaos in the transmitted laser signal. Under other parameter conditions for both NH3 and SF6 a rich variety of optically bistable effects were observed obtained in systems as small as 1 mm for SF64,5.

DOI
10.1364/idlnos.1985.tuc3

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There has been considerable interest over the last few years in transitions to chaos in passive optically bistable systems. Ikeda1 showed in 1979 that an optically bistable ring resonator containing the simplest of nonlinear systems, a two-level media, can show a period doubling route to chaos. This was demonstrated by us2 using NH3 gas near resonantly pumped by pulsed CO2 laser radiation. More generally we identified and demonstrated the unique advantages of molecular gases in this field, providing in particular a vast range of laser-molecular coincidences together with control of response time, and therefore switching time and modulation frequency, by varying gas pressure. Subsequent extension of this work to all optical Fabry-Perot resonators revealed huge oscillatory effects3 leading to chaos in the transmitted laser signal. Under other parameter conditions for both NH3 and SF6 a rich variety of optically bistable effects were observed obtained in systems as small as 1 mm for SF64,5.
Dispersive optical bistability and instabilities leading to period doubling, higher harmonics, and chaos in an all-optical passive quantum system are discussed theoretically and experimentally. These phenomena have been observed for a wide range of operating conditions in ring and Fabry-Perot resonators containing ammonia molecular gas as the nonlinear medium. Laser input intensity, gas pressure, and cavity tuning are the main control parameters in observation of these effects. The experimental results are well modeled by our generalization of standard two-level system theory to include standing-wave, reservoir, and transverse effects.
This chapter concludes the discussion about temporal instabilities and self-oscillations, considering the instabilities that arise in the systems analyzed in Chapter 13, with the exception of optical bistability, which has been discussed separately in Chapter 11. Section 25.1 focuses on the laser with an injected signal. As already mentioned in Section 13.1, in this system self-pulsing instabilities are rather ubiquitous, and on exploring the parameter space one meets an extremely rich variety of oscillatory behaviors. For example, under extremely high-gain conditions, breathing, spiking and chaos have been identified over various ranges of the driving field strength [294]. In this section we show some results that arise under parametric conditions that are more accessible experimentally. We illustrate especially the coexistence, for the same parametric values, of different oscillatory behaviors that are reached by starting from different initial conditions. On the other hand, Section 25.2 deals with a laser with a saturable absorber. In this system even the full scenario of stationary intensity solutions in the single-mode model is very complex. For the sake of simplicity, in this section we focus on a simpler rate-equation model that is obtained from the single-mode model of Eqs. (13.13)–(13.17) by adiabatically eliminating the atomic polarization of both active and passive medium. As in Chapter 13, we assume that the atomic transition frequencies are equal and also coincide with a cavity frequency. In this way all the variables in the model can be assumed real, and the linearization around the stationary solution described in Section 13.2 leads to a cubic eigenvalue equation. The spontaneous oscillations which arise from this instability are called repetitive passive Q-switching in the literature. Section 25.3 considers the stability of the stationary solutions of the degenerate optical parametric oscillator described in Section 13.4 and outlines the scenario of period doubling and chaos that arises under appropriate parametric conditions.